There are two types of symmetry: "Layer Symmetry" and "Symmetric Modeling". I think you mixed them up (which isn't bad, but one should know about it).
'Symmetric Modeling' keeps you control cage symmetric on both sides - Your comment reads, like this is what you actually want. However, it seems like you have somehow killed that history command, because obviously, the control cage isn't symmetric anymore. That can happen, if you are modifying the limit surface patches with tools that don't support history. You should have seen a dialog, that actually asks you, whether you want to proceed. But as this happens quite often and isn't a bad thing, you probably just hit 'ok'. After deleting the 'symmetric modeling' history command (by pressing ok), you deleted some control faces on one half of the car, hence, the car isn't symmetric anymore. Happens...
Now, how to get them back: You need to recreate them - and yes, your idea is correct. Delete the rest of the half, too, and use Edit > Duplicate > Mirror. Turn on 'Merge Subdivs' and make sure the mirror plane is set correctly. After that your Subdiv control cage is symmetric again, BUT there is no history, that will keep it symmetric. For that use Object Edit > Symmetric Modeling again. Now everything should be be kept symmetric again.
The other type of symmetry is 'Layer Symmetry'. This is completely unrelated and can be used to mirror the limit surfaces, but NOT the controls. The surfaces mirrored by layer symmetry will be shown with dashed lines. It seems like you used BOTH types at the same time, which is possible, but most of the time not wanted. (For example it makes sense to use both, if you want a symmetric cage, but you also have features on the limit surface, that you want to mirror, like trimming.) You can enable/disable layer symmetry in the layer bar, in the object lister, or in the 'Layers' menu. Since you are confused by 'dotted lines' you probably want to disable it.
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